Formally, we assume that a trusted central generator \(G_{\rm server}\)  synthesizes images from a set of \(N\)  federated clients. Each client \(C_i \) , for \( i \in [N]\)  consists a locally trained discriminator \(D_i\) , and a generator \(G_i\) . \(G_i\)  takes random Gaussian noise \(z\)  and conditional label \(\tilde{y}\)  as inputs to generate synthetic images, and \(D_i\)  distinguish the synthetic image \(\tilde{x}=G(z, \tilde{y})\)  v.s. private image \(x\)  and its real label \(y\) . We keep \(D_i\)  locally and adopt FedAvg [1]} to aggregate \(G_i\)  to \(G_{\rm server}\) , namely,
\(G_{\rm server} = \sum _{i=1}^N w_iG_i,\) 
